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If 2tana=3tanb then to prove sin(a+b)=5sin(a-b). Pls help in this ques because I have found no similar question on the net.

If 2tana=3tanb then to prove sin(a+b)=5sin(a-b). Pls help in this ques because I have found no similar question on the net.

Grade:10

2 Answers

SRC Jayanth
57 Points
4 years ago
Given 
2tana = 3 tanb
2 sina /cosa = 3 sinb / cosb
by cross multiplying
2sina cosb = 3 sinb cosa 
multiplying 2 on both sides
4sina cosb = 6 sinb cosa
5sina cosb- sina cosb = 5sinb cosa + 1 sinb cosa
 
bringing terms with integral coefficient – 5  on to one side
then we get
5 (sina cosb - sinb cosa)=  sina cosb +  sinb cosa
Which on applying transformation
5 sin (a -b)= sin(a+b)
Hence we got the required.
Shashank Raut
25 Points
4 years ago
2sinA/cosA = 3sinB/cosBcross multiple2sinAcosB=3sinBcosA2{sin(A+B)+sin(A-B)}= 3{sin(A+B)+sin(B-A)}Solve furtherTry to put more efforts because trigonometry will not come until you give maximum 20 minutes and minimum 15min

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